Elliptic curve isogeny class 200.1-e over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-200.1-e
• Conductor: 200.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 200.1-e over \(\Q(\sqrt{11}) \)

Isogeny class 200.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
200.1-e1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 18\) , \( 52 a + 173\bigr] \)
200.1-e2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 117 a - 387\) , \( 1500 a - 4975\bigr] \)
200.1-e3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 7 a - 22\) , \( 29 a - 96\bigr] \)
200.1-e4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 57 a - 197\) , \( -336 a + 1119\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph